Saturday, May 17, 2014

Modelling This Time is Different: Corrected

The first is that I put Probability in the utility function. Generally, this is a no no where the E[utility]=sum over i: P(outcome i)*U(outcome i). I therefore changed it to a more simple maximization problem (no Lagrangian multipliers necessary) where the individual maximizes E[Profits].

The second problem has to deal with maximizing subject to probabilities. Since I sampled from the joint posterior distribution of unknown parameters, I had a number of draws from the distribution. What I did in the previous analysis was maximize each pair of simulated draws individually, and then averaged over these maximized results to get what I thought was the optimal result. In general, this method does not result in the optimal value. I should have maximized all pairs simultaneously. Basically I did E[max s of f(s,p)] instead of max s of E[f(s,a)].

In general, the results are superficially similar to my original analysis. Even if the results are largely the same, its best to describe my mistakes upfront, and avoid awkward questions later.